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Chapter 30 | Atomic Physics
45. (a) What is the minimum value of 1 for a subshell that has 11 electrons in it?
(b) If this subshell is in the shell, what is the spectroscopic notation for this atom?
46. (a) If one subshell of an atom has 9 electrons in it, what is the minimum value of ? (b) What is the spectroscopic
55. Integrated Concepts
Calculate the velocity of a star moving relative to the earth if you observe a wavelength of 91.0 nm for ionized hydrogen capturing an electron directly into the lowest orbital (that is, a
to , or a Lyman series transition). 56. Integrated Concepts
In a Millikan oil-drop experiment using a setup like that in
Figure 30.9, a 500-V potential difference is applied to plates separated by 2.50 cm. (a) What is the mass of an oil drop having two extra electrons that is suspended motionless by the field between the plates? (b) What is the diameter of the drop, assuming it is a sphere with the density of olive oil?
57. Integrated Concepts
What double-slit separation would produce a first-order
maximum at for 25.0-keV x rays? The small answer
indicates that the wave character of x rays is best determined by having them interact with very small objects such as atoms and molecules.
58. Integrated Concepts
In a laboratory experiment designed to duplicate Thomson’s determination of , a beam of electrons having a
velocity of enters a
magnetic field. The beam moves perpendicular to the field in a path having a 6.80-cm radius of curvature. Determine
from these observations, and compare the result with the known value.
59. Integrated Concepts
Find the value of , the orbital angular momentum quantum
number, for the moon around the earth. The extremely large value obtained implies that it is impossible to tell the difference between adjacent quantized orbits for macroscopic objects.
60. Integrated Concepts
Particles called muons exist in cosmic rays and can be created in particle accelerators. Muons are very similar to electrons, having the same charge and spin, but they have a mass 207 times greater. When muons are captured by an atom, they orbit just like an electron but with a smaller radius,

notation for this atom, if this subshell is part of the shell?
47. (a) List all possible sets of quantum numbers
for the shell, and determine the
number of electrons that can be in the shell and each of its subshells.
(b) Show that the number of electrons in the shell equals and that the number in each subshell is .
48. Which of the following spectroscopic notations are not
allowed? (a) (b) (c) (d) (e) . State which rule is violated for each that is not allowed.
49. Which of the following spectroscopic notations are allowed (that is, which violate none of the rules regarding
values of quantum numbers)? (a) (b) (c) (d) (e)
50. (a) Using the Pauli exclusion principle and the rules relating the allowed values of the quantum numbers
, prove that the maximum number of electrons in a subshell is .
(b) In a similar manner, prove that the maximum number of electrons in a shell is 2n2.
51. Integrated Concepts
Estimate the density of a nucleus by calculating the density of a proton, taking it to be a sphere 1.2 fm in diameter. Compare your result with the value estimated in this chapter.
52. Integrated Concepts
The electric and magnetic forces on an electron in the CRT in
Figure 30.7 are supposed to be in opposite directions. Verify this by determining the direction of each force for the situation shown. Explain how you obtain the directions (that is, identify the rules used).
53. (a) What is the distance between the slits of a diffraction grating that produces a first-order maximum for the first Balmer line at an angle of ?
(b) At what angle will the fourth line of the Balmer series appear in first order?
(c) At what angle will the second-order maximum be for the first line?
54. Integrated Concepts
A galaxy moving away from the earth has a speed of . What wavelength do we observe for an to
transition for hydrogen in that galaxy?
since the mass in
is (a) Calculate the radius of the orbit for a muon in a
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207.
uranium ion ( ).
(b) Compare this with the 7.5-fm radius of a uranium nucleus. Note that since the muon orbits inside the electron, it falls into a hydrogen-like orbit. Since your answer is less than the radius of the nucleus, you can see that the photons emitted as the muon falls into its lowest orbit can give information about the nucleus.
61. Integrated Concepts
Calculate the minimum amount of energy in joules needed to create a population inversion in a helium-neon laser
containing moles of neon.